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Routledge eBooks

Observables, measurements and uncertainty

Sander Bais

Published Oct 1, 2025• 0 citations
Publisher

Abstract

It is wrong to think of that past [ascribed to a quantum phenomenon] as ‘already existing’ in all detail. The past is theory. The past has no existence except as it is recorded in the present. By deciding what questions our quantum registering equipment shall put in the present we have an undeniable choice in what we have the right to say about the past.

DOI
10.4324/9781003701910-8

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It is wrong to think of that past [ascribed to a quantum phenomenon] as ‘already existing’ in all detail. The past is theory. The past has no existence except as it is recorded in the present. By deciding what questions our quantum registering equipment shall put in the present we have an undeniable choice in what we have the right to say about the past.
Abstract An open quantum system leaks information into its environment. We are interested in physical situations where an observer, say Alice, can recover some of that information, as a classical measurement record. The optimal way for Alice to estimate the quantum state at time t from the record before t is known as quantum filtering. Recently, a version of quantum smoothing, in which Alice estimates the state at time t using her record on both sides of t , has been developed. It requires Alice to make optimal inferences about the pre- t record of a second observer, say Bob, who recovers whatever information Alice does not. But for Alice to make this inference, she needs to know Bob’s measurement setup. In this paper we consider what happens if Alice is mistaken in her assumption about Bob’s setup. We show that the accuracy—as measured by the trace-squared-deviation, of Alice’s estimate of the true state (i.e. the state conditioned on her and Bob’s pre- t records)—depends strongly on her setup, Bob’s actual setup, and the wrongly assumed setup. Using resonance fluorescence as a model system, we show numerically that in some cases the wrong smoothing is almost as accurate as the right smoothing, but in other cases much less accurate, even being less accurate than Alice’s filtered estimate. Curiously, in some of the latter cases the fidelity of Alice’s wrong estimate with the true state is actually higher than that of her right estimate. We explain this, and other features we observe numerically, by some simple analytical arguments.
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The Witness Hypothesis questions "the existence of time without observers." Can we truly say that "past events" like the beginning of the universe—which no one witnessed—really happened? Starting from this simple question, it asks whether Block Universe theory can claim completeness while the scope of "everything already exists" remains ambiguous. The time of stones, the past of rivers, the beginning of a universe without observers—do they "exist," or are they "treated as non-existent"? This hypothesis stands at that boundary, gently offering a question to which no one has an answer. Keywords: Observation Problem, Block Universe Theory, Ontology of Time, Philosophy, Interpretation of Quantum Mechanics